Question

Fie multimile:A=(2n+1,3n-1) si B=(4n-5,n+5).Determinati n∈N astfel incat A=B.
Va rog....

Answer 1

adica
2n+1=4n-5
2n-4n=-5-1
-2n=-6
2n=6=>n=6:2=>n=3
adica sa formenz multimea a fac
2n+1=2x3+1=6+1=7
3n-1=3x3-1=9-1=8
multimea a={7,8}
sa formez multimea b fac
4n-5=4x3-5=12-5=7
n+5=3+5=8
deci multimea b={7,8}

2n+1=n+5
2n-n=-1+5
n=4
adica sa formez multimea a fac
2n+1=2x4+1=8+1=9
3n-1=3x4-1=12-1=11
deci multimea a={9,11}
sa formez multimea b fac
4n-5=4x4-5=16-5=11
n+5=4+5=9
deci multimea b={9,11}
 de mai jos se repeta exact
3n-1=4n-5
3n-4n=-5+1
-n=-4=>n=4

3n-1=n+5
3n-n=5+1
2n=6=>n=3
din tot deducem ca pt n=3 a={7,8} si b={7,8}
pt n=4 a={9,11} si b={9,11}